The works [1]}, [2]} provide conditions for the existence and uniqueness of invariant measures in for general evolution equation of reaction-diffusion type. Their approach is based on the results of Krylov and Bogoliubov [3]} on the tightness of a family of measures. The key ingredients of this approach include the Feller property and stochastic continuity of the Markov semigroup \(P_t\) , and the existence of least one solution which is globally bounded in certain probability sense [4]}, [5]}, [6]}.
The existence of invariant measures for bidomain equation (REF ) using the aforementioned procedure was established in [7]}. In particular, we showed that the equation (REF ) has a stationary solution, which, in turn, implies the existence of invariant measure, defined on the functional space \((u,w) \in H \times H\) . The sufficient conditions for the uniqueness of this invariant measure were also derived in [7]}.
